At every instant, it's got a location given by the vector R;

在每一个瞬时它的位置由位矢 R 给出
R itself is contained in a pair of numbers, x and y,

R 本身包含了一对坐标值 x 和 y
and they vary with time.

并且它们都随着时间的变化而变化
When you vary time a little bit and ask,

当你把时间改变一个微元然后问
"How does R change?"

"位矢 R 会怎样变化"
and you take the quotient of ΔR to Δt,

然后你用 ΔR 比上 Δt
you get the velocity vector.

就可以得到速度矢量
Mathematically, it's done by taking the expression for R and

从数学上看是这样的写出 R 的表达式
differentiating everything in sight

并对所有可以进行矢量微分的部分
that can be differentiated as vector t.

对时间 t 求微商
Even though we started with a single vector,

即使我们从单个矢量出发
which is the position vector,

即位置矢量